Overview
- Covers with great detail the mathematical developments in total variation based image restauration
- Contains a full analysis of quasilinear parabolic equations whose operator is in divergence form, being the subdifferential of a convex function of the modulus of the gradient
Part of the book series: Progress in Mathematics (PM, volume 223)
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About this book
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2003.
This book contains a detailed mathematical analysis of the variational approach to image restoration based on the minimization of the total variation submitted to the constraints given by the image acquisition model. This model, initially introduced by Rudin, Osher, and Fatemi, had a strong influence in the development of variational methods for image denoising and restoration, and pioneered the use of the BV model in image processing. After a full analysis of the model, the minimizing total variation flow is studied under different boundary conditions, and its main qualitative properties are exhibited. In particular, several explicit solutions of the denoising problem are computed.
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Keywords
Table of contents (7 chapters)
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Front Matter
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Back Matter
Reviews
"This book is well written…[and] should be of interest to anyone studying image reconstruction and to anyone in PDEs trying to see what kinds of modern applications abound for the subject."
—Mathematical Reviews
"This book is devoted to PDE's of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters.... The book is written with great care, paying also a lot of attention to the bibliographical and historical notes. It is a recommended reading for all researchers interested in this field."
—Zentralblatt Math
"The goal of this mongraph is to present general existence and uniqueness results for quasilinear parabolic equations whose operator is the subdifferential of a convex Lagrangian which has linear growth. Special emphasis is given to the case of the minimizing total variational flow for which the Neumann, Dirichlet, and Cauchy problem are discussed. The developed techniques apply to problems in continuum mechanics, image restoration and faceted crystal growth."
---Monatshefte für Mathematik
Authors and Affiliations
Bibliographic Information
Book Title: Parabolic Quasilinear Equations Minimizing Linear Growth Functionals
Authors: Fuensanta Andreu-Vaillo, José M. Mazón, Vicent Caselles
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-7928-6
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel AG 2004
Hardcover ISBN: 978-3-7643-6619-3Published: 26 January 2004
Softcover ISBN: 978-3-0348-9624-5Published: 30 October 2012
eBook ISBN: 978-3-0348-7928-6Published: 06 December 2012
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XIV, 342
Topics: Partial Differential Equations, Approximations and Expansions, Functional Analysis, Visualization, Calculus of Variations and Optimal Control; Optimization